I imagine that this is a very big issue for you. But it's not as bad as you think.
You said that you DO get erections but not at the right time, right? Well good news! That means your equipment is in working order! Have you ever ejaculated? You said that you don't masturbate but have you ever had a wet dream or an experience with another girl-and you DID ejaculate?
Most likely this is psychological. Something is holding you back from having a sexual relationship with this girl. You just have to figure what that something is. Easier said then done, right? Just look deeply into yourself - try to remember what it was that you were thinking when she went down on you. We're you thinking, "Please work..please work!!!" The more you worry about your penis getting erect lessens the chance that it will.
Have you had sex before? Maybe you feel like you're not ready.
Anyway, think about this stuff and good luck.